Using the two given solutions and the general absolute value function we will get:
|x + 9| = 27
Which absolute value function has that solution set?
The two solutions are:
x = 0 and x = -18.
Remember that the absolute value equation is something like:
|x - a| = b
If we want to have these solutions, then:
|0 - a| = b
|-18 -a| = b
From the first one, we have:
|-a| = b
Replacing that on the second equation we get:
|-18 -a| = |-a|
Notice that if we take a = -9, then we have:
|-18 + 9| = |+9|
|-9| = |+9|
This is true, so a = -9.
Then we find the value of b:
|18 + 9| = b = 27
Then the absolute value equation is:
|x + 9| = 27
If you want to learn more about absolute value equations, you can read.
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